The 25th seed dropped her level in the second set but raced through the decider in just 26 minutes to win 6-3, 3-6, 6-0 and set up a last-eight meeting with either Aryna Sabalenka or Naomi Osaka.
"It's definitely a huge moment for me, I'm super happy," said Shnaider. "I'm super proud of myself for being for the first time in the quarter-finals."
The exit of Keys, the 2025 Australian Open winner, means Sabalenka and Osaka are the only two Grand Slam champions left in either the men's or women's singles draws at Roland Garros.
Shnaider's previous best run at a major was a fourth-round appearance at the 2024 US Open.